Correct formula to use for potential difference?

[outxbreak]

My book can't stick to one formula EVER.
In Q7 They start off using: E = −ΔV Δs (equation 20-4)

Then magically go to: ΔV = EΔs

Where is the negative sign because it never states to find the magnitude of the potential difference

http://img198.imageshack.us/img198/6914/msbn.jpg



I don't see how ΔV is directionless because in problem 3 it takes on the negative sign


http://img90.imageshack.us/img90/6047/pa9.gif

 

[rude man]

You copied one of the equations wrong: you wrote " E = - ΔV Δs. "

Here's the story: (vectors in bold)

the correct formula is V2 - V1 = ΔV = - E*Δs where Δs is defined positive pointing from point 1 to point 2
and E is the force on a 1 Coulomb charge anywhere between points 1 and 2.

BUT: the 1 coulomb charge is assumed to not affect the given E field. So, more correctly,
E = limit as q → 0 of (force on a positive charge q)/q.

Example: capacitor plates with positive voltage on plate 2 and negative voltage on plate 1.
s points from plate 1 to plate 2.
ΔV = V2 - V1 = -E*Δs > 0.
where Δs is positive since we're going from 1 to 2.
So E = - ΔV/Δs which would be negative. The force on a small positive test charge q is always qE so the force is negative and points in the direction opposite to Δs.